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Nature of Swaps

A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

An Example of a “Plain Vanilla” Interest Rate Swap

- An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million
- Next slide illustrates cash flows

---------Millions of Dollars---------

LIBOR

FLOATING

FIXED

Net

Date

Rate

Cash Flow

Cash Flow

Cash Flow

Mar.1, 1998

4.2%

Sept. 1, 1998

4.8%

+2.10

–2.50

–0.40

Mar.1, 1999

5.3%

+2.40

–2.50

–0.10

Sept. 1, 1999

5.5%

+2.65

–2.50

+0.15

Mar.1, 2000

5.6%

+2.75

–2.50

+0.25

Sept. 1, 2000

5.9%

+2.80

–2.50

+0.30

Mar.1, 2001

6.4%

+2.95

–2.50

+0.45

Cash Flows to Microsoft(See Table 6.1, page 127)Converting a liability from

fixed rate to floating rate

floating rate to fixed rate

Converting an investment from

fixed rate to floating rate

floating rate to fixed rate

Typical Uses of anInterest Rate SwapFinancial Institution is Involved(Figure 6.4, page 129)

4.985%

5.015%

5.2%

F.I.

MS

Intel

LIBOR+0.1%

LIBOR

LIBOR

Dealer spread = .03% evenly split

Financial Institution is Involved(See Figure 6.5, page 129)

4.985%

5.015%

4.7%

F.I.

MS

Intel

LIBOR-0.25%

LIBOR

LIBOR

Dealer spread = .03 %

Floating

AAACorp

10.00%

6-month LIBOR + 0.30%

BBBCorp

11.20%

6-month LIBOR + 1.00%

The Comparative Advantage Argument (Table 6.4, page 132)- AAACorp wants to borrow floating
- BBBCorp wants to borrow fixed

The Comparative Advantage Argument

- AAACorp has absolute advantage in both markets
- But a comparative advantage in fixed
- BBBCorp has comparative advantage in floating
- If AAA borrows fixed, the gain is 1.2%
- If BBB borrows floating, the gain is reduced by .7%
- Therefore, we have a net gain of 1.2 - .7 = .5%
- If the gain is split evenly, we have a gain per party of: G = (1.2 - .7)/2 = .25%

- Design the swap so AAA’s borrowing rate equals the comparative disadvantage (CD) rate minus the gain:
- LIBOR + .3 - .25
- Do the same thing for BBB
- BBB’s rate with swap:
- 11.2 - .25
- Now, draw the diagram

- Adjust swap gain for dealer spread
- Suppose dealer spread = .04%
- Then gain:
- G = (1.2 - .7 - .04)/2 = .23%
- AAA’s rate with swap:
- LIBOR + .3 - .23 = LIBOR + .07
- BBB’s rate with swap:
- 11.2 - .23 = 10.97%
- Draw swap diagram

The Swap when a Financial Institution is Involved (Figure 6.7, page 133)

9.93%

9.97%

10%

AAA

F.I.

BBB

LIBOR+1%

LIBOR

LIBOR

Check that dealer spread = .04%

Criticism of the Comparative Advantage Argument

- The 10.0% and 11.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates
- The LIBOR+0.3% and LIBOR+1% rates available in the floating rate market are six-month rates
- BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future

Valuation of an Interest Rate Swap

- Interest rate swaps can be valued as the difference between the value of a fixed-rate bond and the value of a floating-rate bond

Swap Valuation

- Fixed Receive: Vswap = Vfixed – Vfloating
- Fixed Pay: Vswap = Vfloating - Vfixed
- The fixed rate stream is valued as an annuity
- The floating rate stream is valued by noting that it is worth par immediately after the next payment date

Floating Rate Perpetuity

- To create a floating rate perpetuity, invest principal value in 6-month LIBOR
- At the end of 6-months, remove the interest and reinvest the principal value at the new 6-month LIBOR
- Therefore, the cost of a floating rate perpetuity is principal value
- It always sells for its par value immediately after interest payment

Floating Rate Instrument with Maturity T

- At the end of T years, floating rate perpetuity is worth the principal value M
- Therefore, the floating rate instrument is worth: M – MdT
- Or M - M/(1+y/2)2T, where is the rate on a zero-coupon bond maturing in T years

Swap Valuation

- The floating rate instrument is worth: Vfloating = M – M/(1+y/2)2T
- The fixed rate stream is worth: Vfixed = (C/2)(Annuity Factor)
- So for Fixed Receive Swap: Vswap = (C/2)(Annuity Factor) - M +M/(1+y/2)2T

Swap Valuation

- The swap is structured such that initial value is zero to either party
- Set Vswap = 0
- Rearrange terms: M=(C/2)(Annuity Factor) + M/(1+y/2)2T
- The left-hand side is the present value of a bond at y
- Since the bond is selling at par, CR = C/M = y
- For the swap to have zero value the fixed rate must equal the yield to maturity on a par bond
- The swap rate is the coupon rate on a LIBOR bond that causes it to be worth par

- Zero coupon LIBOR curve is 5%, 6%, and 7% for one, two, and three years
- What is the swap rate on a three year interest rate swap?
- Assume payments are annual and yields are compounded annually
- Solve for LIBOR par yield
- M = CRxM(d1 + d2 + d3) + Md3

- Solution:

Interest Rate Risk

- Receive Fixed: Vswap = Vfixed – Vfloating
- Pay Fixed: Vswap = Vfloating – Vfixed

An Example of a Currency Swap

An agreement to pay 11% on a sterling principal of £10,000,000 & receive 8% on a US$ principal of $15,000,000 every year for 5 years

Exchange of Principal

- In an interest rate swap the principal is not exchanged
- In a currency swap the principal is exchanged at the beginning and the end of the swap

Three Cash Flow Components

- t = 0: exchange principal based upon current exchange rates Pay: $15 M Rcv: £ 10 M
- t = 1, 2, 3, 4, 5: Pay: .11x10 = £1.1 M Rcv: .08x15 = $1.2 M
- t = 5: Pay: £ 10 M Rcv: $ 15 M

The Cash Flows (Table 6.6, page 140)

Dollars

Pounds

$

£

Years

------millions------

0

–15.00

+10.00

+1.20

1

–1.10

2

+1.20

–1.10

3

+1.20

–1.10

4

+1.20

–1.10

5

+16.20

-11.10

Conversion from a liability in one currency to a liability in another currency

Conversion from an investment in one currency to an investment in another currency

Typical Uses of a Currency SwapAUD

General Motors

5.0%

12.6%

Qantas

7.0%

13.0%

Comparative Advantage Arguments for Currency Swaps (Table 6.7, page 141)General Motors wants to borrow AUD

Qantas wants to borrow USD

Comparative Advantage

- GM has absolute advantage in both markets
- But GM has comparative advantage in dollars
- Qantas has comparative advantage in Australian dollars
- So GM should borrow dollars and Qantas Australian dollars
- Then swap cash flows to earn gain from comparative advantage

Comparative Advantage

- Gain per party: G = (2 - .4)/2 = .8%
- GM’s rate with swap: 12. 6 - .8 = AUD 11.8%
- Qantas’ rate with swap: 7 - .8 = USD 6.2%

- Adjust swap gain for dealer spread
- Suppose dealer spread = .2%
- Then gain:
- Gain per party: G = (2 - .4 - .2)/2 = .7%
- GM’s rate with swap: 12. 6 - .7 = AUD 11.9%
- Qantas’ rate with swap: 7 - .7 = USD 6.3%

USD 5%

USD 6.3%

USD 5%

GM

F.I.

Q

AUD 13%

AUD11.9%

AUD 13%

Check that dealer spread = .2%

Pay: 13.0 – 11.9 = AUD 1.1%

Rcv: 6.3 – 5.0 = USD 1.3%

Valuationof Currency Swaps

Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts

Swaps & Forwards

- A swap can be regarded as a convenient way of packaging forward contracts
- The “plain vanilla” interest rate swap in our example consisted of 6 Fraps
- The “fixed for fixed” currency swap in our example consisted of a cash transaction & 5 forward contracts

Swaps & Forwards(continued)

- The value of the swap is the sum of the values of the forward contracts underlying the swap
- Swaps are normally “at the money” initially
- This means that it costs nothing to enter into a swap
- It does not mean that each forward contract underlying a swap is “at the money” initially

Credit Risk

- A swap is worth zero to a company initially
- At a future time its value is liable to be either positive or negative
- The company has credit risk exposure only when its value is positive

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